There are many induction techniques and not all of them involve a mental effort while trying to fall back asleep.

But if you are trying what you mention, try to make sure you are implementing those with a component that is relaxing or meditative. Whatever you do, your main focus is to relax, and a mantra or visualization should be the secondary focus (at least try it this way). Your sleep itself is still the most important component of lucid dreaming.

For example, try breath in and out slower and slower every time, don't rush it. focus on your inhale and exhale. with every exhale feel like your head is sinking further into your bed.

Binural beats can definitely help fall back asleep.